Problem: A circle with circumference $16\pi$ has an arc with a $\dfrac{5}{4}\pi$ radians central angle. What is the length of the arc? ${16\pi}$ ${\dfrac{5}{4}\pi}$ $\color{#DF0030}{10\pi}$
Answer: The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{5}{4}\pi \div 2 \pi = \dfrac{s}{16\pi}$ $\dfrac{5}{8} = \dfrac{s}{16\pi}$ $\dfrac{5}{8} \times 16\pi = s$ $10\pi = s$